Finite Group Databasebeta

← #29598277

Subgroups — #29598277

Order 15616.

490 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840145C211yesmaximal, characteristic
2C2×#16839579C211yesmaximal, characteristic, complemented
3C2×#16839577C211yesmaximal, characteristic, complemented
4C2×#16839575C211yesmaximal, characteristic
5M32×Dic61C211yesmaximal, characteristic, complemented
6#21445989C211yesmaximal, characteristic, complemented
7C2×C61×#361C211yesmaximal, characteristic
8C22×Dic244C2211yescharacteristic
9C22×#11758200—21no—
10C2×#14519764—21no—
11C2×#14519717C2211yescharacteristic
12#16840145—21no—
13#16840145—21no—
14#16840145C412yes—
15#16840145C412yes—
16C2×#14519713C2211yescharacteristic
17C2×#14519712—21no—
18#16839785—21no—
19C2×C8×Dic61C2211yescharacteristic
20#16839579—22no—
21#16839577—22no—
22#16839575—22no—
23#16839537—21no—
24C16×Dic61—21no—
25C22×D8×C61C2211yescharacteristic
26C2×M32×C61C2211yescharacteristic
27C2×#108×C61C2211yescharacteristic
28C61×#361—22no—
29C22×Dic122—21no—
30C2×Dic244—21no—
31C2×Dic244—21no—
32C2×Dic244—21no—
33C2×Dic244—21no—
34C2×Dic244—21no—
35C2×Dic244C2×C412yes—
36C2×#11758200—22no—
37C2×#11758200—22no—
38C2×#11758200—42no—
39C2×#11758200—42no—
40C2×#11758194—21no—
41C22×#92418D411yescharacteristic
42#14519764—22no—
43#14519764—22no—
44#14519764—42no—
45C2×C22⋊Dic61—42no—
46C2×C4×Dic61D411yescharacteristic
47#14519717—21no—
48#14519717D412yes—
49C2×#11758185—21no—
50#14519713—21no—
51#14519713—21no—
52#14519712—42no—
53#14519706—42no—
54C8×Dic61C2×C411yescharacteristic
55C8×Dic61C2×C411yescharacteristic
56C8×Dic61D411yescharacteristic
57C8×Dic61D411yescharacteristic
58C22×D4×C61—21no—
59C2×D8×C61—21no—
60C2×D8×C61—21no—
61C2×D8×C61—21no—
62C2×D8×C61—21no—
63C2×D8×C61—21no—
64C2×D8×C61C2×C412yes—
65C2×M16×C61—21no—
66C22×C8×C61C2311yescharacteristic
67M32×C61—21no—
68M32×C61D412yes—
69C2×C16×C61—21no—
70#108×C61—21no—
71#108×C61—21no—
72C24×C61—41no—
73C2×D4×C61—22no—
74C2×D4×C61—41no—
75C2×D4×C61—41no—
76C2×D4×C61—41no—
77C2×D4×C61—41no—
78C2×D4×C61—41no—
79C22×C4×C61C2×D411yescharacteristic
80C22×Dic61—41no—
81C22×Dic61SD1612yes—
82C2×Dic122—22no—
83C2×Dic122—41no—
84C2×Dic122—41no—
85C2×Dic122—41no—
86C2×Dic122—41no—
87C2×Dic122—41no—
88D8×C61—22no—
89D8×C61—22no—
90D8×C61—41no—
91D8×C61—41no—
92M16×C61—41no—
93M16×C61—41no—
94C2×C8×C61—41no—
95C2×C8×C61C22×C411yescharacteristic
96C2×C8×C61C2×D411yescharacteristic
97C2×C8×C61C2×D411yescharacteristic
98C2×C8×C61C2×D411yescharacteristic
99C2×C8×C61#4111yescharacteristic
100C2×C8×C61#4111yescharacteristic
101C22⋊Dic61—44no—
102C22⋊Dic61—44no—
103#11758200—44no—
104#11758200—44no—
105C4×Dic61C22⋊C411yescharacteristic
106C4×Dic61C22⋊C411yescharacteristic
107C4×Dic61D812yes—
108#11758194—41no—
109#11758194—41no—
110C2×#92418—41no—
111C2×#92418C22⋊C411yescharacteristic
112C2×#92418C22⋊C411yescharacteristic
113C2×#92418D812yes—
114C2×#92418SD1612yes—
115Dic244—22no—
116Dic244—22no—
117Dic244—41no—
118Dic244—41no—
119C16×C61—22no—
120#11758185—22no—
121C23×C61—42no—
122C23×C61—84no—
123C23×C61—81no—
124C23×C61—81no—
125C23×C61C2×SD1611yescharacteristic
126D4×C61—42no—
127D4×C61—42no—
128D4×C61—81no—
129D4×C61—81no—
130C2×C4×C61C2×C22⋊C411yescharacteristic
131C2×C4×C61#12411yescharacteristic
132C2×C4×C61#12711yescharacteristic
133C2×C4×C61C2×D811yescharacteristic
134C2×C4×C61C2×D811yescharacteristic
135C2×C4×C61C2×SD1611yescharacteristic
136C2×Dic61—42no—
137C2×Dic61—42no—
138C2×Dic61—81no—
139C2×Dic61—81no—
140C2×Dic61#10212yes—
141C2×Dic61#10212yes—
142Dic122—42no—
143Dic122—42no—
144Dic122—81no—
145Dic122—81no—
146C8×C61—81no—
147C8×C61C4×D411yescharacteristic
148C8×C61C4×D411yescharacteristic
149C8×C61#12111yescharacteristic
150C8×C61#12111yescharacteristic
151#92418—81no—
152#92418#10212yes—
153#92418#10212yes—
154#13214—611nomaximal, Sylow
155C22×C61—22no—
156C22×C61—84no—
157C22×C61—82no—
158C22×C61—162no—
159C22×C61—162no—
160C22×C61C2×#10211yescharacteristic
161C22×C61#48611yescharacteristic
162C22×C61#49211yescharacteristic
163C4×C61#39011yescharacteristic
164C4×C61C2×#10211yescharacteristic
165C4×C61#48611yescharacteristic
166C4×C61#49311yescharacteristic
167Dic61—22no—
168Dic61—22no—
169Dic61—82no—
170C2×#495—611no—
171C2×#362—611no—
172C2×#362—611no—
173C2×#361—611no—
174C2×#361D6111yescharacteristic
175C4×M32—611no—
176#1848—611no—
177C2×C61—21no—
178C2×C61—21no—
179C2×C61—162no—
180C2×C61#195711yescharacteristic
181C2×C61#214812yes—
182C22×Q16—611no—
183C22×SD16—1221no—
184C22×D8C2×D6111yescharacteristic
185C2×#124—1221no—
186C2×M32—611no—
187C2×M32C2×D6111yescharacteristic
188#495—612no—
189#495—612no—
190#495—1221no—
191#495—1221no—
192C2×#108—611no—
193C2×#108—1221no—
194C2×#108C2×D6111yescharacteristic
195#423—1221no—
196C2×C4×C8—611no—
197#362—1222no—
198#362—1222no—
199#361—22no—
200#361—1222no—
201#346—1221no—
202C4×C16—1221no—
203C61#1321411yescharacteristic, complemented, Sylow
204C22×Q8—1221no—
205C22×D4—21no—
206C2×Q16—612no—
207C2×Q16—1221no—
208C2×Q16—1221no—
209C2×Q16—1221no—
210C2×Q16—1221no—
211C2×Q16—1221no—
212C2×SD16—1222no—
213C2×SD16—1222no—
214C2×SD16—2442no—
215C2×SD16—2442no—
216C2×D8—21no—
217C2×D8—21no—
218C2×D8—21no—
219C2×D8—21no—
220C2×D8—21no—
221C2×D8C4×D6112yes—
222C2×M16—21no—
223C2×M16—1221no—
224C22×C8—611no—
225C22×C8C22×D6111yescharacteristic
226#124—1222no—
227#124—1222no—
228#124—2442no—
229C2×C22⋊C4—2442no—
230C2×C42—611no—
231M32—21no—
232M32—612no—
233M32—1221no—
234M32C22⋊D6112yes—
235C2×C16—21no—
236C2×C16—1221no—
237#108—21no—
238#108—21no—
239#108—1221no—
240#108—1221no—
241#108—2442no—
242C4⋊C8—2442no—
243C4×C8—611no—
244C4×C8—611no—
245C4×C8—611no—
246C4×C8—611no—
247C24—41no—
248C2×Q8—1222no—
249C2×Q8—2441no—
250C2×Q8—2441no—
251C2×Q8—2441no—
252C2×Q8—2441no—
253C2×Q8—2441no—
254C2×D4—22no—
255C2×D4—41no—
256C2×D4—41no—
257C2×D4—41no—
258C2×D4—41no—
259C2×D4—41no—
260C22×C4—612no—
261C22×C4—2441no—
262C22×C4D4×D6111yescharacteristic
263Q16—1222no—
264Q16—1222no—
265Q16—2441no—
266Q16—2441no—
267SD16—2444no—
268SD16—2444no—
269D8—22no—
270D8—22no—
271D8—41no—
272D8—41no—
273M16—41no—
274M16—41no—
275M16—2441no—
276M16—2441no—
277C2×C8—41no—
278C2×C8—611no—
279C2×C8—611no—
280C2×C8—612no—
281C2×C8—612no—
282C2×C8—2441no—
283C2×C8C2×C4×D6111yescharacteristic
284C2×C8#1175822211yescharacteristic
285C2×C8D4×D6111yescharacteristic
286C2×C8D4×D6111yescharacteristic
287C2×C8#1175822411yescharacteristic
288C2×C8C2×C22⋊D6111yescharacteristic
289C22⋊C4—2444no—
290C22⋊C4—2444no—
291C42—611no—
292C42—611no—
293C42—612no—
294C16—22no—
295C16—1222no—
296C23—42no—
297C23—84no—
298C23—81no—
299C23—81no—
300C23SD16×D6111yescharacteristic
301Q8—4881no—
302Q8—4881no—
303Q8—2442no—
304Q8—2442no—
305D4—42no—
306D4—42no—
307D4—81no—
308D4—81no—
309C2×C4—612no—
310C2×C4—612no—
311C2×C4—4881no—
312C2×C4—4881no—
313C2×C4—2442no—
314C2×C4—2442no—
315C2×C4C22⋊C4×D6111yescharacteristic
316C2×C4#1451976311yescharacteristic
317C2×C4#1451977311yescharacteristic
318C2×C4D8×D6111yescharacteristic
319C2×C4D8×D6111yescharacteristic
320C2×C4SD16×D6111yescharacteristic
321C8—81no—
322C8—612no—
323C8—612no—
324C8—4881no—
325C8#1451973711yescharacteristic
326C8C4×C22⋊D6111yescharacteristic
327C8#1451974911yescharacteristic
328C8#1451975011yescharacteristic
329C22—22no—
330C22—84no—
331C22—82no—
332C22—162no—
333C22—162no—
334C22#102×D6111yescharacteristic
335C22#1684010711yescharacteristic
336C22#1684013311yescharacteristic
337C4—1222no—
338C4—1222no—
339C4—4882no—
340C4#1683966211yescharacteristic
341C4#102×D6111yescharacteristic
342C4#1684010711yescharacteristic
343C4#1684013711yescharacteristic
344C2—21no—
345C2—21no—
346C2—162no—
347C2#2144662311yescharacteristic
348C2#2144756512yes—
subgroupG/H
centerC22#102×D61
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC2×C61×#361C2
socleC22×C61C2×#102
prime radicalC22×D8×C61C22
cosocleC22×C8×C61C23
hypercenterC2×#361D61
hypocenterC61#13214
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#361

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#16839579C2semidirect
3. C2×#16839577C2semidirect
5. M32×Dic61C2semidirect
6. #21445989C2semidirect
203. C61#13214semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#168401452
C2×#168395792
C2×#168395772
C2×#168395752
M32×Dic612
#214459892
C2×C61×#3612
#1321461